§21.10(ii) Riemann Theta Functions Associated with a Riemann Surface

In addition to evaluating the Fourier series, the main problem here is to
compute a Riemann matrix originating from a Riemann surface. Various approaches
are considered in the following references:

•

Belokolos et al. (1994, Chapter 5) and references therein. Here the
Riemann surface is represented by the action of a Schottky group on a region of
the complex plane. The same representation is used in Gianni et al. (1998).

•

Tretkoff and Tretkoff (1984). Here a Hurwitz system is chosen to represent
the Riemann surface.